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An enhanced SDOF model to predit the behaviour of a steel column impacted by a rigid body
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.ORCID iD: 0000-0003-2104-382X
2017 (English)In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 152, p. 771-789Article in journal (Refereed) Published
Abstract [en]

The transient dynamic response of a steel beam-column subjected to impact loading is a complex phenomenon involving large localized plastic deformations and non-smooth contact interactions. Exposed to high intensity of the contact force generated from impact, the beam-column may undergo large displacement and inelastic deformation. Previous research has shown that a calibrated elasto-plastic single degree of freedom system is able to reproduce both the displacement and the force time-history of a steel beam subjected to non-impulsive loading or low-velocity impact. In these models, the static force-displacement curve is derived from either experiments or detailed 3D nonlinear analysis. Tri-linear resistance function has been extensively used to reproduce the different stages of the response including catenary effects. A rigorous treatment of such a complex problem calls for the use of non-smooth analysis tools to handle the impulsive nature of the impact force, the unilateral constraint, the impenetrability condition and the discontinuity of the velocity in a rigorous manner. In this paper, we present a non-smooth elasto-plastic single degree of freedom model under impact loading that permits the use of arbitrary resistance function. Adopting the non-smooth framework offers tools such as differential measures and convex analysis concepts to deal with unilateral contact incorporating Newton’s impact law. The mid-point scheme is adopted to avoid numerical unrealistic energy decay or blowup. Furthermore, the non-penetration condition is numerically satisfied by imposing the constraint at only the velocity level to guarantee energy-momentum conservation [1]. The explicit expression of resistance functions of the beam that are used in the SDOF model are obtained from a simplified nonlinear static analysis of two beam-column models. In the analysis, a linear relation between normal force and bending moment is assumed for the plastification of the hinges. Two proposals to simplify the explicit expressions of the model’s response behavior are given. Performing an energy-based analysis, we predict maximum displacement that is needed to absorb the kinetic energy arising from the impact for different coefficient of restitution. The numerical examples underline the validity of the model by showing good agreement with the predictions of reference models.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 152, p. 771-789
Keywords [en]
Single degree of freedom, Impact, Non-smooth analysis, Steel structures, Catenary action, Analytical solution
National Category
Building Technologies
Identifiers
URN: urn:nbn:se:kth:diva-217277DOI: 10.1016/j.engstruct.2017.08.061Scopus ID: 2-s2.0-85042169401OAI: oai:DiVA.org:kth-217277DiVA, id: diva2:1154935
Note

QC 20171106

Available from: 2017-11-06 Created: 2017-11-06 Last updated: 2018-02-27Bibliographically approved
In thesis
1. Simplified mechanical models for the nonlinear dynamic analysis of elasto-plastic steel structures impacted by a rigid body
Open this publication in new window or tab >>Simplified mechanical models for the nonlinear dynamic analysis of elasto-plastic steel structures impacted by a rigid body
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Buildings subjected to impact and explosion are usually studied using large scale and highly nonlinear finite element model which are time-consuming. The first part of the thesis deals with the development of simple and accurate models for evaluating the nonlinear inelastic behaviour of steel frame structures subjected to impact. The research work in this part has produced four simplified models. The first model concerns with a 4DOF model that reproduces the behaviour of the impacted column. The restraining effect from the rest of the structure is modelled by an elastic spring, a head mass and a static load applied at the top of the column. In the second model, the impacted column is then further simplified using a SDOF model. The behaviour of the SDOF model is governed by an analytical force-displacement expressions of the column loaded by a located force. The maximum displacement of the impacted column can also be determined explicitly by adopting an energy-equivalent approach. Afterwards, in an effort to model the whole structure, two finite element models are developed. For these models, a co-rotational super-element that consists of a beam element and two generalized elasto-plastic hinges is obtained by performing a static condensation. An elastic flexible beam element is used in the first finite element model, whereas a rigid beam element is considered in the second one.

In these models, inelasticity is concentrated at generalized elasto-plastic hinges which are modelled by combined axial-rotational springs. The behaviour of the hinges is uncoupled in the elastic range while an axial-bending interaction is considered in the plastic range making it possible to reproduce a wide range of cross-sections and joints. In addition, unilateral contact between rigid point masses is considered and the energy loss during impact is accounted by means of a restitution coefficient following Newton’s impact law. Energy-momentum scheme is used to solve the equations of motion produced by these models.

The second part of the thesis concerns with the performance of the connectors in composite steel-concrete slabs under explosion. The purpose is to determine residual capacities of the shear connectors after being damaged by explosion using large-scale pull-out and push-out experimental tests and finite element simulations.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. p. 176
Series
TRITA-BKN. Bulletin, ISSN 1103-4270 ; 151
National Category
Building Technologies
Research subject
Civil and Architectural Engineering
Identifiers
urn:nbn:se:kth:diva-217281 (URN)
Public defence
2017-12-08, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20171106

Available from: 2017-11-06 Created: 2017-11-06 Last updated: 2017-11-07Bibliographically approved

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Battini, Jean-Marc

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